class: center, middle, inverse, title-slide .title[ #
Predicting Covid-19 infections using multi-layer centrality measures
] .subtitle[ ##
Master Thesis
] .author[ ### Christine Hedde - von Westernhagen ] .date[ ### 22-05-2023
Program MSBBSS, Department of Methodology and Statistics, Utrecht University
Supervisors: Javier Garcia-Bernardo, Ayoub Bagheri
] --- class: center, middle, inverse # **Predicting Covid-19 infections** <span style = "color:darkslategray";> using multi-layer centrality measures </span> --- class: middle .pull-left[.center[ <img src="data:image/png;base64,#img/net_animation.gif" width="100%" /> ]] ### <p style="margin:250px 0px 0px 550px"> Model spread to inform policy decisions! <br><br> <b>Who</b> gets infected and <b>when</b>? </p> --- class: center, middle, inverse # <span style = "color:darkslategray";> Predicting Covid-19 infections using </span> **multi-layer** <span style = "color:darkslategray";> centrality measures </span> --- class: left, top ### Our lives are multi-layered. <img src="img/3dplot_dummy.png" style="height:450px; width:700px; object-fit:cover; border:5px white; margin:10px 0px 15px 30px"> <p style="margin:-400px 0px 0px 800px"> <b> CBS micro-data </b> allows to construct multi-layer network dataset. <br><br> Micro-data can be linked to <b> PCR test data. </b> <br><br> Analyses conducted on regional <b> subset</b> of ~ 1m nodes. </p> --- class: center, middle, inverse # <span style = "color:darkslategray";> Predicting Covid-19 infections using multi-layer </span> **centrality measures** --- class: left, top <br> <img src="img/Degree.png" style="width:400px; margin:0px 0px 0px 0px"> -- <img src="img/Eigenvector.png" style="width:400px; margin:0px 0px 0px -50px"> -- <img src="img/PageRank.png" style="width:400px; margin:0px 0px 0px -50px"> --- class: center, middle, inverse # **Single-layer centrality <br> ≠ <br> Multi-layer centrality ** --- class: left, middle <figure> <img src="img/multilayer_dedomenico_cut.png" style="width:750px; margin:35px 0px -10px 150px"> <figcaption style="font-size:15px; margin:0px 0px -10px 150px"> <i>De Domenico et al. 2015, Supplementary Figure 1</i> </figcaption> </figure> <br><br> ---- <p style="font-size:15px">De Domenico, M., Solé-Ribalta, A., Omodei, E., Gómez, S., & Arenas, A. (2015). Ranking in interconnected multilayer networks reveals versatile nodes. Nature Communications, 6(1), 6868. https://doi.org/10.1038/ncomms7868 </p> --- class: left, top, inverse ## **Bringing it all together:** <br><br><br> > ## How well can multi-layer centrality measures predict the infection of individuals with epidemic diseases like Covid-19? --- class: center, middle, inverse # **Analytic Strategy** --- class: left, top ### *Outcome*: **Time until infection** ### *Predictors*: Degree, Eigenvector, PageRank<br> ----------------------------------------------------- -- 1. ### Simulate an epidemic on the network k = 500 -- 2. ### Get time until infection for the nodes in each simulation -- 3. ### Run prediction models for each of the 500 data sets and compute estimates -- #### a. Rank correlations `\(\rho\)` of centrality measures and outcome -- #### b. Uno's Concordance Index `\(C\)` of Cox models including linear combinations of centralities as predictors -- #### c. `\(R^2\)` of linear models including linear combinations of centralities as predictors -- 4. ### Average the estimates across simulations --- class: center, middle, inverse # **Results** --- class: left, top <br><br> ### a. **Medium negative correlations** of all centrality measures with outcome <br> -- ### b. **Concordance index ~ 0.85** for predictor combinations including Degree centrality and/or PageRank <br> -- ### c. ~ **15% of variance** explained in outcome by (at least) Degree `\(^2\)` <br> -- <br> ### **Also**: Only small differences between single-layer and multi-layer measures. --- class: center, middle, inverse # **Is that it?** --- class: left, top <br><br> ## Multiple layers, multiple transmission rates. -- <b> ### **➔** **Weighted Degree centrality** -- <br><br> ### ...minimal performance increase --- class: center, top, inverse <br><br><br><br><br><br><br> # **...what about the real infection data?** --- class: center, top, inverse <br><br><br><br><br><br><br> # **<span style = "color:darkslategray";> ...what about the real infection data? </span>** ### `$$R^2 \le 0.01$$` --- class: center, middle, inverse # **Lessons learned** --- class: left, top, clear <br> > ### Centrality measures can predict **relative infection risks** well, but are limited in predicting the **timing of infections**. -- <br><br> > ### Multi-layer measures don't seem to offer great benefits. -- <br><br> > ### Administrative data is not sufficient to model social contacts. --- class: left, top, clear <br> > ### <span style = "color:lightgray";>Centrality measures can predict relative infection risks well, but are limited in predicting the timing of infections.</span> <br> > ### <span style = "color:lightgray";>Multi-layer measures don't seem to offer great benefits.</span> <br> > ### <span style = "color:lightgray";>Administrative data is not sufficient to model social contacts.</span> <br> ### Centrality measures could still **complement** prediction models -- ### ... **if** used with representative contact networks. --- class: center, middle, inverse # **Backup slides** --- class: left, top #### Behind the scenes: **Simulating an epidemic** on a large-scale network using a SIR model. `$$\frac{dS}{dt} = -\beta I S$$` `$$\frac{dI}{dt} = \beta I S - \gamma I$$` `$$\frac{dR}{dt} = \gamma I$$` #### Each node can be in one of the **three states**, and **transitions stochastically** based on *network contacts*, *transmission rate*, and *recovery time*. `$$S \rightarrow I$$` `$$I \rightarrow R$$` #### Where the transmission probabilities for the nodes in layer `\(l\)` at time `\(t\)` is given by: `$$\pmb{\tau'}_{lt} = 1 - (1 - \tau_l)^\mathbf{\Gamma_{t-1}}$$` --- class: left # Do you have... ### 👩👴👶👦...many close relatives? (Degree Centrality) <br> ### 👩👴👶👦 👭 👧👴👵👦...many close relatives and also a partner with a big family? (Eigenvector Centrality)<br> ### ✈️🌍 👧👴👵👦... but that partner's family lives in a different country? (Betweenness Centrality) <br> <br> ###... then you could be a **super-spreader**. <br> ### High centrality **⇝** High spreading capacity ### ***But***: High spreading capacity **≠** High infection risk <!-- to build incremental slides as separate pages in PDF --> <style type="text/css"> @media print { .has-continuation { display: block; } } </style>